In math, is rounding and estimating the same thing?

Discussion in 'General Education' started by heavens54, Oct 7, 2010.

  1. heavens54

    heavens54 Connoisseur

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    Oct 7, 2010

    I am not sure...is there a subtle difference in the two actions? How do you teach the difference in the two actions? Are they different strategies or basically the same? Thanks.
     
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  3. clarnet73

    clarnet73 Moderator

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    Oct 7, 2010

    estimating= your best guess
    rounding isn't a guess.

    however... when I'm estimating how much I'm spending at the store, I use rounding as a tool in my estimation.
     
  4. Ms. I

    Ms. I Maven

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    Oct 7, 2010

    They're pretty much the same. I agree that rounding is the best way to estimate.
     
  5. blazer

    blazer Connoisseur

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    Oct 7, 2010

    Birmingham to Chicago approx 4000 miles. That is an estimate

    mm in one inch 25.54 or rounded to 25.5

    They are not the same thing.
     
  6. 3Sons

    3Sons Enthusiast

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    They're not the same.

    Rounding is used when you have a number already and want to alter it. If I have a restaurant check of $29.52 and need to add an appropriate tip, I first round up to $30. That's not an estimate, I know quite well the bill is actually $29.52. Then I divide by 6 to get $5. Why six? Because I know dividing things by six gives an estimate of a 17% tip, which is pretty reasonable. I get $5, which is that estimate. I can then add it to the bill exactly to get $34.52 or I can keep my rounded up $30 and pay $35 total.
     
  7. amakaye

    amakaye Enthusiast

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    Some of my students are currently struggling with this concept--we keep reviewing the fact that we sometimes round in order to estimate. We took an index card and wrote out an addition problem (say, 47+31). We then rounded the numbers, and labeled them as "rounded numbers." Then we added those to get our "estimate." Finally, we solved for our "exact answer." Seeing how the parts related to each other really helped it click for several.
     
  8. knitter63

    knitter63 Groupie

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    In EDM, estimating is to the 10,100, or 1000. It is the best guess. Rounding is NOT the same thing! The only part of "rounding" that goes into estimating is that the student "rounds" to the nearest 10,100 or 1000.
     
  9. stargirl

    stargirl Companion

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    Rounding is a strategy used to estimate. My math series (Scott-Foresman) gives rounding and front-end estimation as estimation strategies. I show my students how to do front end (basically just take the first digit of the number and turn the rest to zeroes, so that 276 would become 200) but show them that rounding will give them a closer estimate.
     
  10. robinsky

    robinsky Rookie

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    Oct 8, 2010

    Rounding is a specific mathematical concept, and there is only one way to do it. You need to specify which place a number should be rounded to. For example, 6.745 rounded to the nearest tenth would be 6.7 (because the next place, hundredths, is a 4, which rounds down). If you had specified to the nearest hundredth, it would be 6.75 (because the thousandths digit is 5, which rounds up).

    Estimating doesn't really have one specific right answer, but there are strategies to doing it, like the tip example above of dividing by 6.
     
  11. terptoteacher

    terptoteacher Connoisseur

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    Off topic, but I would round to 30. 10% OF 30 is 3.00, so 20% would be 6.00. So then I would estimate that 5.00 is a good tip....more than 15% but less than 20%. I'm not a math person and it's kinda cool that my weird way is pretty good!!!
     
  12. jday129

    jday129 Comrade

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    Oct 9, 2010

    No, estimating can be used in lots of different situations. I can look at a jar of marbles and estimate how many are in the jar. I can estimate how far I jogged based on the time it took me and how hard I was running. Estimating is taking information that is known and using it to come up with a guess for information that is not known.
    Rounding is used when specific data is known, but the numbers are not easy to work with (such as a dinner bill for $38.46). I can round to the nearest dollar or ten dollars and make the data simpler for further calculations.
     
  13. beccmo

    beccmo Comrade

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    Oct 10, 2010

    I teach science, and we round all the time due to significant figures rules. I tell my students to look at the entire number to the right of their last significant figure to determine how they round. If they are more than half way to the next number, round up, less than half way, round down. If they are exactly half way they must round to the EVEN number.

    Just looking at one number right of the cut off won't work all the time. 5.5501 rounded to the nearest hundredth is 5.55, but rounded to the nearest tenth is 5.6.
     
  14. ecl

    ecl Rookie

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    I am in no way saying this to be offensive, but to shine a light on a weakness in teacher education programs.

    The fact that a certified teacher can ask this question makes a good case for having all teachers become certified in math.
     
  15. Genmai

    Genmai Companion

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    Oct 10, 2010

    Estimation is an important skill because it is practical. For middle school kids, I find that it is important to explain why estimation is very useful and worth learning. Take this example:

    You go to store to buy some groceries. You only have $5 and don't have a calculator. You can estimate before you haul stuff to the cash register to make sure that you have enough. Here is what you have in your basket so far:

    1 carton of eggs: $1.69
    1 carton of juice: $1.69
    1 carton of ice cream: $1.50

    Do you have enough? It's hard to tell with these numbers so we estimate by changing a few prices by rounding.

    cost of eggs: 1.69 --> 1.70
    cost of juice: 1.69 --> 1.70
    cost of ice cream: 1.50 --> 1.50

    From the changed numbers, it is easier to use mental math and see that we have enough money.

    Sum 1.70 and 1.70, and we get 3.40
    Add 1.50 to the subtotal and we get $4.90

    * Important *
    We rounded UP so we know that our estimate is LOWER than the final amount that rings up at the cashier. If we rounded down, what can you say about the final estimate? What if we rounded some prices up and some prices down, what do you think happens to the final estimate? why?

    You can also do estimates with fractions, for taxes and bunch of other things. This is a useful and practical skill.

    :2cents:
     

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